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Domain decomposition preconditioners for Schur complement systems arising in structured nonlinear optimization problems.

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Title: Domain decomposition preconditioners for Schur complement systems arising in structured nonlinear optimization problems.
Authors: Lueg, Laurens R.1 (AUTHOR), Bynum, Michael L.2 (AUTHOR), Laird, Carl D.1 (AUTHOR), Biegler, Lorenz T.1 (AUTHOR) biegler@cmu.edu
Source: Optimization & Engineering. Mar2026, Vol. 27 Issue 1, p555-585. 31p.
Subjects: Domain decomposition methods, Schur complement, Parallel programming, Mathematical optimization, Nonlinear programming, Iterative methods (Mathematics), Interior-point methods
Abstract: Large-scale nonlinear, nonconvex optimization problems arise in many relevant engineering applications, such as integrated energy systems, public health, or supply-chain logistics. Their solution is often challenging due to problem scale, significant spatio-temporal interactions, or time constraints (e.g. for real-time operations). This work focuses on decomposition strategies for nonlinear problems with distributed structure, where interactions between problem partitions can be defined over sparse graphs. Parallelization is achieved on the linear algebra level within an interior point algorithm using the Schur complement method, and we propose several distributed algebraic preconditioners for the Schur complement system, based on approaches from the field of domain decomposition. We demonstrate promising strong scaling results on large-scale problem instances for parameter estimation of infectious disease models and PDE-constrained optimal control. [ABSTRACT FROM AUTHOR]
Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 191978998
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  Data: Domain decomposition preconditioners for Schur complement systems arising in structured nonlinear optimization problems.
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  Data: <searchLink fieldCode="JN" term="%22Optimization+%26+Engineering%22">Optimization & Engineering</searchLink>. Mar2026, Vol. 27 Issue 1, p555-585. 31p.
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  Data: <searchLink fieldCode="DE" term="%22Domain+decomposition+methods%22">Domain decomposition methods</searchLink><br /><searchLink fieldCode="DE" term="%22Schur+complement%22">Schur complement</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+programming%22">Nonlinear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Interior-point+methods%22">Interior-point methods</searchLink>
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  Data: Large-scale nonlinear, nonconvex optimization problems arise in many relevant engineering applications, such as integrated energy systems, public health, or supply-chain logistics. Their solution is often challenging due to problem scale, significant spatio-temporal interactions, or time constraints (e.g. for real-time operations). This work focuses on decomposition strategies for nonlinear problems with distributed structure, where interactions between problem partitions can be defined over sparse graphs. Parallelization is achieved on the linear algebra level within an interior point algorithm using the Schur complement method, and we propose several distributed algebraic preconditioners for the Schur complement system, based on approaches from the field of domain decomposition. We demonstrate promising strong scaling results on large-scale problem instances for parameter estimation of infectious disease models and PDE-constrained optimal control. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Optimization & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s11081-025-10020-1
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      – Code: eng
        Text: English
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        PageCount: 31
        StartPage: 555
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      – SubjectFull: Domain decomposition methods
        Type: general
      – SubjectFull: Schur complement
        Type: general
      – SubjectFull: Parallel programming
        Type: general
      – SubjectFull: Mathematical optimization
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      – SubjectFull: Nonlinear programming
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      – SubjectFull: Iterative methods (Mathematics)
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      – SubjectFull: Interior-point methods
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      – TitleFull: Domain decomposition preconditioners for Schur complement systems arising in structured nonlinear optimization problems.
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              Text: Mar2026
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              Y: 2026
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